{"title":"关于一个 2х2 算子矩阵的基本谱成分数","authors":"M. I. Muminov, I. Bozorov, T. Rasulov","doi":"10.26907/0021-3446-2024-2-85-90","DOIUrl":null,"url":null,"abstract":"In this paper, a 2х2 block operator matrix H is considered as a bounded and self-adjointoperator in a Hilbert space. The location of the essential σess(H) of operator matrix H is described via the spectrum of the generalized Friedrichs model, i.e. the two- and three-particle branches of the essential spectrum σess(H) are singled out. We prove that the essential spectrum σess(H) consists of no more than six segments (components).","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"408 2‐3","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the number of components of the essential spectrum of one 2х2 operator matrix\",\"authors\":\"M. I. Muminov, I. Bozorov, T. Rasulov\",\"doi\":\"10.26907/0021-3446-2024-2-85-90\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, a 2х2 block operator matrix H is considered as a bounded and self-adjointoperator in a Hilbert space. The location of the essential σess(H) of operator matrix H is described via the spectrum of the generalized Friedrichs model, i.e. the two- and three-particle branches of the essential spectrum σess(H) are singled out. We prove that the essential spectrum σess(H) consists of no more than six segments (components).\",\"PeriodicalId\":507800,\"journal\":{\"name\":\"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika\",\"volume\":\"408 2‐3\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26907/0021-3446-2024-2-85-90\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26907/0021-3446-2024-2-85-90","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文将 2х2 块算子矩阵 H 视为希尔伯特空间中的有界自关节算子。通过广义弗里德里希模型的谱来描述算子矩阵 H 的本质σess(H) 的位置，即本质谱 σess(H)的两粒子和三粒子分支。我们证明了本质谱 σess(H) 由不超过六个分段（成分）组成。
On the number of components of the essential spectrum of one 2х2 operator matrix
In this paper, a 2х2 block operator matrix H is considered as a bounded and self-adjointoperator in a Hilbert space. The location of the essential σess(H) of operator matrix H is described via the spectrum of the generalized Friedrichs model, i.e. the two- and three-particle branches of the essential spectrum σess(H) are singled out. We prove that the essential spectrum σess(H) consists of no more than six segments (components).
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